G\"{o}del and G\"{o}del-type universes in K-essence theory

In this paper, the G"{o}del-type solutions within the k-essence theory are investigated. The consistency of field equations, causality violation and existence of closed timelike curves are studied. The conditions for existence of G"{o}del and G"{o}del-type solutions are determined for any function that defines the k-essence. By taking different sources of matter, it is shown that this theory of gravity allows causal and non-causal G"{o}del-type solutions.